@jrbartendersorry for the late reply here! You are absolutely correct that a taller boot tends to give more support to your ankles.
That being said, I am not seeing anywhere on REI's website that measures the height of boot, although I could be missing it. If I am missing it, please point it out, so I can better help. Typically REI has divided our Hiking Boot categories into types: Hiking Shoes, Day Hiking Boots and Backpacking Boots.
Typically, Backpacking Boots will have a higher cut to them and will tend to have a stiffer midsole, providing better support and more stability.
As you decide what kind of boot to choose for your trip, here are some questions for you to think about:
How much weight are you carrying on your back? A light daypack or a heavy backpack? The heavier the pack, the heavier duty a boot you will need. You might tend toward a taller, stiffer, backpacking boot in this case.
What kind of terrain? The rougher and rockier the terrain, the more you might tend toward a taller boot with a stiffer midsole.
Do you have any known ankle injuries or are you prone to rolling your ankles? A taller, more supportive boot might offer more protection.
How much break in time do you have before your trip? A heavier duty boot requires more break in time.
Some boots will be approximately the same height but might offer different midsoles or internal support. Boots that have a shank or a polyurethane midsole tend to be stiffer, while EVA tends to have more cushion and be lighter.
Also, the best boot for someone is the one that fits correctly! Make sure you buy your boots with plenty of break in time before your trip. At REI, we also offer one-on-one Boot Fitting Services. Your local green vests would love to help you find the perfect fitting boot!
I'll throw out one more tip: Trekking Poles. I LOVE my trekking poles. They keep me upright more often than not (I'm clumsy) and they also provide support!! Check out this Expert Advice Article on How to Choose Trekking Poles.
Also, it sounds like these boots are for a trip to Machu Picchu?! That sounds amazing!! I hope it is a trip of a lifetime! Feel free to attach a picture of your trip to this thread once you've gone and come back!